Sandwich results for higher order fractional derivative operators

Zayed, H. M.; Bulboacă, Teodor

doi:10.15330/ms.49.1.52-66

Cited by 4 publications

(5 citation statements)

References 7 publications

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“…ematicians based on subordinate techniques, for instance, Zayed and Bulboacă [39], Attiy et al [40], Lupaş and Oros [41], Reem and Kassim [42], Abdulnabi et al [43], Oros and Oros [44], Oros [45], and others. On the other hand, the study of interesting geometric attributes associated with some families of special functions has attracted a lot of investigators and experts, such as Merkes and Scott [46] in 1961, who examined starlike hypergeometric functions.…”

Section: Proposed Logarithm-hurwitz-lerch Zeta Functionmentioning

confidence: 99%

“…In other words, this principle acts as a gist tool of the holomorphic class of functions in which characterizations of functions are inferred from a differential stipulation. Recently, advanced studies have been extensively conducted by famed mathematicians based on subordinate techniques, for instance, Zayed and Bulboacă [39], Attiy et al [40], Lupaş and Oros [41], Reem and Kassim [42], Abdulnabi et al [43], Oros and Oros [44], Oros [45], and others. On the other hand, the study of interesting geometric attributes associated with some families of special functions has attracted a lot of investigators and experts, such as Merkes and Scott [46] in 1961, who examined starlike hypergeometric functions.…”

Section: Introductionmentioning

confidence: 99%

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Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Abdulnabi,

F. Al-Janaby,

Ghanim

et al. 2024

Symmetry

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The interest in special complex functions and their wide-ranging implementations in geometric function theory (GFT) has developed tremendously. Recently, subordination theory has been instrumentally employed for special functions to explore their geometric properties. In this effort, by using a convolutional structure, we combine the geometric series, logarithm, and Hurwitz–Lerch zeta functions to formulate a new special function, namely, the logarithm-Hurwitz–Lerch zeta function (LHL-Z function). This investigation then contributes to the study of the LHL-Z function in terms of the geometric theory of holomorphic functions, based on the differential subordination methodology, to discuss and determine the univalence and convexity conditions of the LHL-Z function. Moreover, there are other subordination and superordination connections that may be visually represented using geometric methods. Functions often exhibit symmetry when subjected to conformal mappings. The investigation of the symmetries of these mappings may provide a clearer understanding of how subordination and superordination with the Hurwitz–Lerch zeta function behave under different transformations.

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Section: Proposed Logarithm-hurwitz-lerch Zeta Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Abdulnabi,

F. Al-Janaby,

Ghanim

et al. 2024

Symmetry

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show abstract

“…In effect, interesting recent studies have emanated about dealing with subordinate and superordinate techniques and sandwiches problems correlated with numerous complex operators, for instance, Atshan et al [17], Sokół et al [18], Zayed and Bulboacă [19], Al-Janaby and Ahmad [20], Mishra and Soren [21], Al-Janaby and Darus [22], Al-Janaby et al ( [23], [24]), Ghanim and Al-Janaby ( [25], [26]), Attiy ([27], [28]), Lupaş and Oros [29] and Atshan ( [30], [31]).…”

Section: Introduction Issn: 0067-2904mentioning

confidence: 99%

Sandwich Subordinations Imposed by New Generalized Koebe-Type Operator on Holomorphic Function Class

Moureh,

Al-Janaby

2023

Iraqi Journal of Science

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In the complex field, special functions are closely related to geometric holomorphic functions. Koebe function is a notable contribution to the study of the geometric function theory (GFT), which is a univalent function. This sequel introduces a new class that includes a more general Koebe function which is holomorphic in a complex domain. The purpose of this work is to present a new operator correlated with GFT. A new generalized Koebe operator is proposed in terms of the convolution principle. This Koebe operator refers to the generality of a prominent differential operator, namely the Ruscheweyh operator. Theoretical investigations in this effort lead to a number of implementations in the subordination function theory. The tight upper and lower bounds are discussed in the sense of subordinate structure. Consequently, the subordinate sandwich is acquired. Moreover, certain relevant specific cases are examined.

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“…Recently, in other studies, [48][49][50][51][52][53][54]60 the authors obtained differential subordination results for multivalent functions within a generalized fractional calculus. The main idea of the technique we use here involves investigating the geometric properties of functions in [p] employing a novel convolution operator.…”

Section: Introductionmentioning

confidence: 99%

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

Morais

Zayed

Srivastava

2021

Math Methods in App Sciences

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We propose third‐order differential subordination results associated with new admissible classes of multivalent functions defined in the open unit disk on the complex plane. Besides, we investigate the geometric properties of multivalent functions associated with a novel convolution operator. This is done by taking suitable linear combinations of the classical Gaussian hypergeometric function and its derivatives up to third‐order and applying the Hadamard product (or convolution) formula for power series. The complex velocity potential and the stream function of two‐dimensional potential flow problems over a circular cylinder using both sources with sink and two sources are treated by the methods developed in the present paper. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of source/sink is also source/sink for a given complex potential. Finally, some plot simulations are provided to illustrate the different results of this work.

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Sandwich results for higher order fractional derivative operators

Cited by 4 publications

References 7 publications

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Sandwich Subordinations Imposed by New Generalized Koebe-Type Operator on Holomorphic Function Class

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

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